{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PVOLXWVAQ32X6IJCTIMDZR44B2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0db6c1ef372fcc623e957b3f621217b3080206418c91330cdc306ee1231351ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-08-22T14:01:56Z","title_canon_sha256":"4c8471d2ba048bd655799e5bfbcdcb2690c45314a35dcefab4a1d4289550953c"},"schema_version":"1.0","source":{"id":"2508.16400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.16400","created_at":"2026-07-05T11:57:47Z"},{"alias_kind":"arxiv_version","alias_value":"2508.16400v1","created_at":"2026-07-05T11:57:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.16400","created_at":"2026-07-05T11:57:47Z"},{"alias_kind":"pith_short_12","alias_value":"PVOLXWVAQ32X","created_at":"2026-07-05T11:57:47Z"},{"alias_kind":"pith_short_16","alias_value":"PVOLXWVAQ32X6IJC","created_at":"2026-07-05T11:57:47Z"},{"alias_kind":"pith_short_8","alias_value":"PVOLXWVA","created_at":"2026-07-05T11:57:47Z"}],"graph_snapshots":[{"event_id":"sha256:3314f6efbf740f68e440bfd907c7fb161923b45e3e26d79f5bd2e12b160a4643","target":"graph","created_at":"2026-07-05T11:57:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.16400/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that all natural numbers $n\\equiv 4\\pmod 6$ are the sum of two Chen primes (primes $p$ such that $p+2$ has at most two prime factors), apart from a power-saving set of exceptions. This improves on various previous results and is optimal, barring substantial progress on the twin prime or binary Goldbach conjectures.\n  The proof is based on constructing a non-negative model for the Chen primes in a suitable approximate sense. To do this, we develop an efficient sieving strategy that makes use of a power-saving variant of the Bombieri--Vinogradov theorem. Furthermore, we show that the pri","authors_text":"Joni Ter\\\"av\\\"ainen, Lasse Grimmelt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-08-22T14:01:56Z","title":"The Exceptional Set in Goldbach's Problem with two Chen Primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.16400","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:06c86edfa67c0c22759341d0419eca41d0f9b79651ef706b5ed70d79f0dbbbc2","target":"record","created_at":"2026-07-05T11:57:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0db6c1ef372fcc623e957b3f621217b3080206418c91330cdc306ee1231351ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-08-22T14:01:56Z","title_canon_sha256":"4c8471d2ba048bd655799e5bfbcdcb2690c45314a35dcefab4a1d4289550953c"},"schema_version":"1.0","source":{"id":"2508.16400","kind":"arxiv","version":1}},"canonical_sha256":"7d5cbbdaa086f57f21229a183cc79c0e854f6b9b250530a9bcf2f7c941641013","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d5cbbdaa086f57f21229a183cc79c0e854f6b9b250530a9bcf2f7c941641013","first_computed_at":"2026-07-05T11:57:47.580373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:57:47.580373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gBrWFZvrNjvNpvjwA4feQk2WuYbIYo/RMUxwJ5+2thl5RCTS363il4OKAlNJNJ/p7AcoRVaSbF/fxHndemVjDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:57:47.580810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.16400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06c86edfa67c0c22759341d0419eca41d0f9b79651ef706b5ed70d79f0dbbbc2","sha256:3314f6efbf740f68e440bfd907c7fb161923b45e3e26d79f5bd2e12b160a4643"],"state_sha256":"d271d55b4f741b120dae4157b0ef1e889b4743029f72ebe2ac9a9dc357ebb8cf"}